Just wondering

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Just wondering

Postby darthbadass » Thu Mar 30, 2006 11:32 pm

Anyone have a Definitive way to visualize 4D in your mind, and if so could you share it? I've come close but it's all just 3D in the end.
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Postby jinydu » Fri Mar 31, 2006 1:28 am

While I don't know of a definitive way to actually visualize 4D (at least not one that has worked for me), such a capability is not strictly necessary for working with 4D. You can develop full-fledged 4D geometry and calculus without any visualization. As far as I know, most (though not all) people who work with 4D don't claim to be able to visualize it.
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Re: Just wondering

Postby DenijsD » Thu Apr 13, 2006 9:38 am

darthbadass wrote:Anyone have a Definitive way to visualize 4D


The human brain isn't equipped to see or sense the fouth D. Nor is it equipped to see or sense 2D, which is easier to imagine though. Yet there is nobody, I am sure, who can describe how 2D beings would communicate, or even see or sense each other. :)
There isn't a 4th dimension? I think, do you?
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Re: Just wondering

Postby bo198214 » Thu Apr 13, 2006 10:46 am

DenijsD wrote:The human brain isn't equipped to see or sense the fouth D. Nor is it equipped to see or sense 2D, which is easier to imagine though.


You mix things up. The question was about visualization, that is imagenation. You refer to sense and see, which is quite different. Imagining the geometric relations in a plane is quite easy for humans to perform, 3d is already a bit more difficult and 4d is really hard (or impossible for most humans).

Yet there is nobody, I am sure, who can describe how 2D beings would communicate, or even see or sense each other. :)


Its only your lack of imagenation ;)
How 2D-Beings would live is already several times discussed also on this forum. Its a bit like playing god and invent worlds (mainly physical laws generalized from our world) for 2D inhabitants. See for example the constructions we made for duonians based on magnetism in 2D.
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Re: Just wondering

Postby DenijsD » Thu Apr 13, 2006 11:46 am

bo198214 wrote:Its only your lack of imagenation ;)


:D

It probably is! I like to say it differently, though. :wink:

What I meant to say is. It is so hard to visualise a 2d or 4d universe, because it's so hard to imagine what it would be like. And it is so hard to imagine because we are not equipped to look at things that way, we simply don't need to do so to survive.
That doesn't mean that it is good fun to try to visualise the 4th dimension. In time our brains might develop in such a way that we do understand how it all works. But don't worry, then there is the next dimension to be explored :D
There isn't a 4th dimension? I think, do you?
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Postby wendy » Fri Apr 14, 2006 9:40 am

visualising 4d is quite easy. first you make a model of it, and then have a look at it.

Seriously, though, you need to look at some of the methods i give on my website about doing this, of maps and pictures, and looking at things holographically. Even then, you still need to make things that work in 4d. You got to do the necessary modelling in your mind, and see if the maths makes sense.

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Postby moonlord » Fri Apr 14, 2006 6:55 pm

DenijsD: The only limit is human imagination. Set the ruls in a life program, and it will model life for you. The interesting part is that with the rules there are in our world, life is VERY RANDOM. Therefore, we have two hands because God played dice...
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Postby 4D guy » Sun Apr 16, 2006 5:11 pm

I usually compare the 2nd dimension to the 3rd dimension, to get the idea of what it's like. But I think about 4D a little as 3d as well, but when i do that 3d becomes 2d and don't use the lower dimensions.
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Postby ashbox » Mon May 08, 2006 4:19 am

Hi :)

Very new to this discussion, i actually found this site randomly.

Ok, well since this isn't an introduction thread ill spare you my life story. As for imagining how a 4 dimentional object looks, or shape which i believe is a better term, i think borders on extremely hard to impossible.

Over the last few days I've been thinking about how one could imagine such a shape, weather it be based from our 2 dimentional square or circle in some way. I think the furthest ive got is understanding the requirements to picture one and I think thats as far as most people will get, myself included.

Alot of the diagrams shown on this site are very helpful, and the explaination on them has pretty well given me these following thoughts, (i was going to say conclusions, but this topic is far from that).

A 4 dimentional shape, requires you to picture a 3 dimentional one, as one of its "sides". Its important to know in our world or realm we can see the entire side of a 3D object just looking at it. IE. I may view the entire side of my desk, it has a wooden finish, i know this because i can see all of it, it is 2D.

Now to picture a 4D desk, you must somehow imagine this same "side" as a 3D object, with the same capabilities. This time i know more about my desk, i can see behind the 3D side to the back of it by looking at its front.

Im sorry I used front and back, they are big no nos when it comes to explaining how to view a 4D object considering their extreme variations, or existance at all.

Anyways simply put, the side of a 4D object is a 3D object, and that same 3D object inverted at the same time. Something both inside out and not inside out at the same time. Also, if your able to picture this, you are only looking at one side of a 4D object, and one side alone. Looking at multipul sides to a 4D object as you can probably already tell gets much more complex. I havent figured out how edges work, or exist.

Id also like to add that trying to illustrate such an object, i think the closest example i can think of is the impossible triangle prehaps. Even then its only half way there.

Please feel free to cut me up for writing this as if im some professor on the subject, to that i am not of course. I am definatly no expert on this, although i might have acted like a know-it-all in this post. Sorry for any offense taken, and welcome all critism and objections to what i have said.

Thank you for reading my post.
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Postby PWrong » Tue May 30, 2006 9:48 am

Hi

Very new to this discussion, i actually found this site randomly.

Hi Ashbox, welcome to the forum. Sorry for the late reply.

Anyways simply put, the side of a 4D object is a 3D object, and that same 3D object inverted at the same time. Something both inside out and not inside out at the same time.

You're right that the side of a 4D object is a 3D object. I'm not sure what you mean by the object being inverted or inside out. As a 4D being, you could see every part of the 3D side, but always from the same angle. Maybe you've been mislead by the cube-inside-a-cube representation of the tetracube?

I havent figured out how edges work, or exist.

What is it you can't figure out about them?

Id also like to add that trying to illustrate such an object, i think the closest example i can think of is the impossible triangle prehaps. Even then its only half way there.

It might depend on which 4D object you're talking about, but most 4D objects aren't related to the impossible triangle at all, except that they are difficult to visualise.
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